Structural-acoustic sensitivity analysis of fully coupled systems for modification of shell geometry

The optimization of multi-modal objective functions as formulated for complicated structural-acoustic systems is limited by available time as known. Thus, the time to compute the objective function will decisively provide the number of iteration steps. Further, sensitivity analysis will aggravate this problem in gradient-based optimization. Often, the objective function has to be calculated additionally for sensitivity computation via finite differences schemes. To overcome this bottle neck the sensitivities have to be computed more efficiently. If the shell structure is modified geometrically, the stiffness can be affected locally. This modification approach needs only small modification compared with the structural measurement and the acoustic wave length to achieve significant influence on the vibration. Therefore, design variables can be concentrated on the structural system. Furthermore, conditions preventing increase of mass need not be introduced. In this paper, a concept is presented that parameterizes the shell geometry to reduce the number of design variables. Then, the sensitivities with respect to these design variables are computed applying the adjoint variable method. This facilitates to use only the adjoint operator of the structural system for deriving the sensitivities. The structural dynamic response is estimated applying Finite Elements Analysis and the acoustic system is solved by Boundary Elements Method. The acoustic and the structural systems are then coupled via integral conditions enforcing equilibrium at the interface.